Question

Find the gradient of the curve x^2 + 2xy-2y^2 +x=2 at the point (-4,1)

Answer 1

First, you find out partial x and partial y.. do you have that yet?

Answer 2

I'd suggest starting with what is a gradient then go into partial derivatives

Answer 3

Does this help?\[
x^2~+~2xy~-~2y^2~+x~=2 \\
2x+2\frac{\textrm{d}y}{\textrm{d}x}-4\frac{\textrm{d}y}{\textrm{d}x}+1~=~0
\]I can't remember if gradient is the same thing as slope.

Answer 4

gradient means slope in certain context yes; its also a term used to find the normal to a surface

Answer 5

i think you missed your product rule tho

Answer 6

\[x^2~+~2xy~-~2y^2~+x~=2 \]
\[2xx'~+~2x'y+~2xy'~-~4yy'~+x'~=0 \]
if "wrt.x" then x' = dx/dx = 1
\[2x~+~2y+~2xy'~-~4yy'~+1~=0 \]

Answer 7

plug in (-4,1) and solve for y'